_ r=0 ^n 4^r .^n C_r is equal to - Vidyadip

MCQ

$\sum_{r=0}^n 4^r .^n C_r$ is equal to

A
$6^n$
B
$5^{-n}$
C
$4^n$
D
$5^n$

✓

Answer

(d) $5^n$
Explanation: $\sum_{r=0}^n 4^r .^n C_r=4^0 \cdot n C_0+4^1 \cdot n C_1+4^2{ }^n C_2+\ldots+4^n \cdot{ }^n C_n$
$\begin{array}{l}=1+4 \cdot{ }^n C_1+4^2 \cdot{ }^n C_2+\ldots .+4^n \cdot{ }^n C_n \\ =(1+4)^n=5^n\end{array}$

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